Negative global deviance in gamlss? What does a negative global deviance in gamlss mean?
From their book "Flexible Regression and Smoothing", draft is here: 
http://www.gamlss.org/wp-content/uploads/2015/07/FlexibleRegressionAndSmoothingDraft-1.pdf
On page 128, they show the example 

Negative global deviance?? What is that supposed to mean?
And also, is that a good thing? I know we want to minmize deviance, so is negative-deviance ... like, super good?
 A: The same website where you link the document has another publication, where they state that the "Global Deviance is -2*max(log likelihood) under hypotheses H0 and H1 respectively."  I ran a quick test on my own data, and it seems to match that claim:  I ran a simple negative binomial model using gamlss, and it produced a Global Deviance of 6697.049.  I then used logLik() to get the log-likelihood of -3348.524.  If you do the calculation, it works.
http://www.gamlss.com/wp-content/uploads/2018/01/DistributionsForModellingLocationScaleandShape.pdf
Since you want to maximize the log likelihood when comparing models, and GD is the negative of that, it stands to reason that you want to minimize the Global Deviance output from gamlss (which is intuitive, since, as you note, we normally want to minimize 'deviance').  I don't think the negative GD by itself has a specific meaning.  However, from iteration 1 to iteration 11 in your post, your GD is decreasing, which would seem to be a good sign.
